You can mix and match any models that will run Unleashed, but you have to run a controller version that supports all APs in the same Master/Slave group. This means that your bound by the last version for the longest EOL'd AP, which will still (hopefully) works on the newest model(s) you have. In this case, that would be the R500, which means version 200.7.10.102.64 is what you'd have to run on all APs, even though the R510/R610 have newer versions available. As long as your oldest and newest models aren't too many generations apart from one another, it should be fairly easy to find a firmware sub-version that runs well enough on both. Hope that makes sense.
As far as the R6__ versus R5__ models, the 6's have 3x3 stream radios and the 5's have 2x2. That's it; everything else is identical: effective range, number of clients supported, receiving sensitivity, interference mitigation, etc. Typically more bang for your buck with the R5__ stuff, just because most clients out in the real world are 2x2 at the most, unless you have some actual stuff that is 3x3 and would benefit from the bit of extra bandwidth.